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Non-Automatizability of Bounded-Depth Frege Proofs

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Abstract.

In this paper, we show how to extend the argument due to Bonet, Pitassi and Raz to show that bounded-depth Frege proofs do not have feasible interpolation, assuming that factoring of Blum integers or computing the Diffie–Hellman function is sufficiently hard. It follows as a corollary that bounded-depth Frege is not automatizable; in other words, there is no deterministic polynomial-time algorithm that will output a short proof if one exists. A notable feature of our argument is its simplicity.

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Authors and Affiliations

  1. Department of Software (LSI), Universitat Politècnica de Catalunya, Barcelona, Spain

    Maria Luisa Bonet & Ricard Gavaldà

  2. Department of Mathematical and Computing Science, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo, Japan

    Carlos Domingo

  3. Department of Mathematics and Computer Science, Clarkson University, Potsdam, NY, 13699-5815, U.S.A

    Alexis Maciel

  4. Department of Computer Science, University of Toronto, Toronto, Ontario, Canada, M5S 3G4

    Toniann Pitassi

Authors
  1. Maria Luisa Bonet
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  2. Carlos Domingo
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  3. Ricard Gavaldà
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  4. Alexis Maciel
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  5. Toniann Pitassi
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Corresponding author

Correspondence to Maria Luisa Bonet.

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Bonet, M.L., Domingo, C., Gavaldà, R. et al. Non-Automatizability of Bounded-Depth Frege Proofs. comput. complex. 13, 47–68 (2004). https://doi.org/10.1007/s00037-004-0183-5

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  • DOI: https://doi.org/10.1007/s00037-004-0183-5

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